Department of Mathematics & Statistics
Basic Algebra I
- Sept. 2-Sept 6: (Appendix A-D).
Overview of the course. Sets,
relations, and functions.
Induction. Number systems
including complex numbers. Equivalence relations.
- Sept 9-Sept 13: (Chapter 1).
Arithmetic in Z. The division algorithm.
The Euclidean algorithm and gcd's.
Fundamental theorem of arithmetic.
- Sept 16-Sept 20: (Chapter 2).
Congruences. Modular arithmetic. Finite fields.
- Sept 23-Sept 27: (Chapter 3).
Rings. Definitions and basic examples. Isomorphisms and homomorphisms.
- Sept 30-Oct 4: (Chapter 4).
Arithmetic in polynomial rings. Division algorithm and
- Oct 7-Oct 11: (Chapter 4, cont'd).
- Oct 14-Oct 18: Review of the material, and midterm test.
- Oct 21-Oct 25: (Chapter 5).
Congruences in polynomial rings. More on finite fields.
- Oct 28-Nov 1: (Chapter 6).
Ideals and quotient rings.
- Nov 4-Nov 8: (Chapter 9).
Integral Domains. Unique factorization in number rings. Application to
- Nov 11-Nov 15: (Chapter 9).
More on rings, Integral domains, and quadratic integers.
- Nov 18-Nov 22: (Section 7.1-7.5).
Group theory. Definition and basic examples. Subgroups,
isomorphism and homomorphism. Lagrange's theorem.
- Nov 25-Nov 29: (Section 7.6-7.9).
More group theory. Normal subgroups, quotients, and homomorphisms.
- Dec 2-Dec 4:
Review of the material.